Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #2150 |
172 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=e,b^2=d,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^9,h^c=h^16,h^e=h^13,h^f=h^1688 conjugacy classes — view the full character table.
| maximal subgroup of | #17981232, #17981258, #17981330, … |
| maximal normal subgroup of | #17981232, #17981258, #17981330, … |
| maximal quotient of | #17982224, #17982240, #17982257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21699);